Amperian loops

Amperian loops#

A current \(I\) flows around the rectangular loop shown in the figure. Evaluate \(\oint\vec{\mathbf{B}}\cdot d\vec{\mathbf{\ell}}\) for the paths \(A\), \(B\), \(C\), and \(D\).

Rectangular loop of current with four different Amperian loops

Part 1#

Path \(A\):

Answer Section#

  • \(-2\mu_0 I\)

  • \(-\mu_0 I\)

  • zero

  • \(\mu_0 I\)

  • \(2\mu_0 I\)

Part 2#

Path \(B\):

Answer Section#

  • \(-2\mu_0 I\)

  • \(-\mu_0 I\)

  • zero

  • \(\mu_0 I\)

  • \(2\mu_0 I\)

Part 3#

Path \(C\):

Answer Section#

  • \(-2\mu_0 I\)

  • \(-\mu_0 I\)

  • zero

  • \(\mu_0 I\)

  • \(2\mu_0 I\)

Part 4#

Path \(D\):

Answer Section#

  • \(-2\mu_0 I\)

  • \(-\mu_0 I\)

  • zero

  • \(\mu_0 I\)

  • \(2\mu_0 I\)

Attribution#

Problem is from the OpenStax University Physics Volume 2 textbook, licensed under the CC-BY 4.0 license.
Image representing the Creative Commons 4.0 BY license.